Borel completeness of some ℵ₀-stable theories
Michael C. Laskowski ; Saharon Shelah
Fundamenta Mathematicae, Tome 228 (2015), p. 1-46 / Harvested from The Polish Digital Mathematics Library
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We study ℵ₀-stable theories, and prove that if T either has eni-DOP or is eni-deep, then its class of countable models is Borel complete. We introduce the notion of λ-Borel completeness and prove that such theories are λ-Borel complete. Using this, we conclude that an ℵ₀-stable theory satisfies I∞,ℵ₀(T,λ)=2λ for all cardinals λ if and only if T either has eni-DOP or is eni-deep.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:283327 
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Michael C. Laskowski; Saharon Shelah. Borel completeness of some ℵ₀-stable theories. Fundamenta Mathematicae, Tome 228 (2015) pp. 1-46. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-1-1/